The space of real places on ℝ(x, y)



Abstract

The space 𝓜(ℝ(x, y)) of real places on ℝ(x, y) is shown to be path-connected. The possible value groups of these real places are determined and for each one it is shown that the set of real places with that value group is dense in the space. Large collections of subspaces of the space 𝓜(ℝ(x, y)) are constructed such that any two members of such a collection are homeomorphic. A key tool is a homeomorphism between the space of real places on ℝ((x))(y) and a certain space of sequences related to the “signatures” of [2], which themselves are shown here to be related to the “strict systems of polynomial extensions” of [3].


Keywords

real place; space of real places; strict system of polynomial extensions; Harrison set; path-connected; dense subset

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Published : 2018-01-31


BrownR., & MerzelJ. L. (2018). The space of real places on ℝ(x, y). Annales Mathematicae Silesianae, 32, 99-131. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/13916

Ron Brown  ron@math.hawaii.edu
Department of Mathematics, Univeristy of Hawaii, USA  United States
Jonathan L. Merzel 
Department of Mathematics, Soka University of America, USA  United States



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